I've done some digging and determined that it's very possible, and probably quite likely that BuNo.17799 did serve overseas with a combat squadron.
Mark and I discussed the "missing year" factor via e-mail a few weeks back and I decided I would reference the history cards for the ten planes that preceeded BuNo.17799 off the factory line, and the ten planes that came after her. A quick look at the data showed me that the record keeping process during that time was a bit more chaotic and non-standardized that it would be just a few months down the road. They were apparently still working the inefficiencies out of the system amidst the rush to war.
It was very interesting to note that a number of the aircraft from this time period were missing their records starting from the time they rolled off the line, until August of 1944. Something must have happened in July of 1944 that caused this information to be lost, or to be destroyed. Maybe an attack at sea destroyed a critical bulk of paperwork, or maybe it was just an absent mided clerk.

A little more digging will hopefully reveal the answer, as well as the factual history of BuNo.17799 from September 1943 - August 1944.
_____________________________________________________________
F4U-1A BuNo.17789
Accepted: August 31, 1943
Delivered: September 6, 1943
Service History:
ADU / NAS New York, New York (September 9, 1943)
enroute to Pacific Theatre (October 5, 1943)
Pacific Theatre - CFWC (October 23, 1943)
awaiting reconditioning at San Diego (by August 1944)
stricken: September 30, 1944
_____________________________________________________________
F4U-1A BuNo.17790
Accepted: August 28, 1943
Service History:
ADU / NAS Port Columbus, Ohio (shipped: August 31, 1943)
NAS San Diego, California (shipped: September 2, 1943)
VMF-114 (shipped: September 14, 1943)
VMF-441 (shipped: June 9, 1944)
stricken: June 20, 1944
_____________________________________________________________
F4U-1A BuNo.17791
Accepted: August 30, 1943
Service History:
ADU / NAS New York, New York (shipped: September 6, 1943)
NAS San Diego, California (shipped: September 18, 1943)
VMF-217 (shipped: September 29, 1943)
VMF-122 (shipped: February 16, 1944)
stricken: May 31, 1944
_____________________________________________________________
F4U-1A BuNo.17792
Accepted: August 30, 1943
Service History:
ADU / NAS Port Columbus, Ohio (shipped: August 31, 1943)
NAS San Diego, California (shipped: September 2, 1943)
Naumea, New Caledonia (shipped: September 27, 1943)
VMF-222 (November 11, 1943)
VMF-211 (January 18, 1944)
stricken: March 28, 1944
_____________________________________________________________
F4U-1A BuNo.17793
Accepted: August 31, 1943
Delivered: September 6, 1943
Service History:
*gap in history record
unknown (August 1944 – October 1944)
MCAS Quantico, Virginia - Assembly & Repair / Pool (November 1944 – January 1945)
VBF-95 (February 1945)
unreported (March 1945 – April 1945)
CASU-24 (?)
stricken: May 31, 1945
_____________________________________________________________
F4U-1A BuNo.17794
Accepted: August 28, 1943
Delivered: September 2, 1943
Service History:
*gap in history record
NAS Jacksonville, Florida – Assembly & Repair (August 1944 – September 1944)
NAS Glenview, Illinois - CQTU (October 1944 – March 1945)
NAS Jacksonville, Florida - pool (April 1945)
NAS Jacksonville, Florida – under reconditioning (May 1945)
NAS Jacksonville, Florida – pool (June 1945)
reconditioned: June 28, 1945
CASU-33 (July 1945)
“over” - *no further records
_____________________________________________________________
F4U-1A BuNo.17795
Accepted: September 3, 1943
Delivered: September 6, 1943
Service History:
*gap in history record
VF-5 / OTU (August 1944 – June 1945)
Flight Instrument School (July 1945)
NAS Green Cove, Florida – pool (August 1945 – September 1945)
NAS Clinton, Oklahoma (October 1945)
stricken: October 31, 1945
_____________________________________________________________
F4U-1A BuNo.17796
Accepted: August 31, 1943
Delivered: September 6, 1943
Service History:
NAS San Diego, California (shipped: September 14, 1943)
VMF-225 (September 125, 1943)
VMF-251 (December 14, 1943)
stricken: 1944
_____________________________________________________________
F4U-1A BuNo.17797
Accepted: August 30, 1943
Service History:
ADU / NAS Port Columbus, Ohio (shipped: September 2, 1943)
NAS San Diego, California (shipped: September 8, 1943)
Naumea, New Caledonia (shipped: September 27, 1943)
VMF-211 (January 18, 1944)
stricken: March 28, 1944
_____________________________________________________________
F4U-1A BuNo.17798
Accepted: August 31, 1943
Service History:
ADU / NAS New York, New York (September 6, 1943)
NAS San Diego, California (September 20, 1943)
Naumea, New Caledonia (October 2, 1943)
VMF-222 (February 12, 1944)
stricken: May 18, 1944
_____________________________________________________________
F4U-1A BuNo.17799
Accepted: August 31, 1943
Delivered: September 6, 1943
Service History:
*gap in history record
NAS San Diego, California - Assembly & Repair (August 1944 - October 1944)
unreported (December 1944)
VF-84 (December 1945)
VBF-14 (January 1945)
VBF-98 (February 1945 - March 1945)
CASU-33, NAS Los Alamitos, California (April - June 1945)
VBF-84 "Wolf Gang", NAS San Diego, California (July 1945)
CASU-33, NAS Los Alamitos, California (August 1945)
stricken: August 31, 1945
_____________________________________________________________
F4U-1A BuNo.17800
Accepted: August 30, 1943
Delivered: September 2, 1943
Service History:
ADU / NAS Port Columbus, Ohio (arrived: September 2, 1943)
NAS San Diego, California (arrived: September 9, 1943)
VMF-218 (arrived: September 28, 1943)
Naval Air Operations Training (arrived: July 8, 1944)
NAS Jacksonville, Florida – Assembly & Repair (August 1944)
CQTU / NAS Glenview, Illinois (September 1944)
unknown (October 1944)
CQTU / NAS Glenview, Illinois (November 1944)
stricken: November 30, 1944
_____________________________________________________________
F4U-1A BuNo.17801
Accepted: September 3, 1943
Delivered: September 6, 1943
Service History:
*gap in history record
NAS San Diego, California - Assembly & Repair (August 1944 – October 24, 1944)
MCAS Quantico, Virginia (October 27, 1944 – November 1944)
VMBF-931 (November 1944 – December 1944)
VBF-95 (January 1945 – February 1945)
VBF-152 (March 1945 – April 19, 1945)
Elizabeth City, North Carolina
Unreported (April 1945)
VBF-3 (May 1945)
stricken: June 30, 1945
_____________________________________________________________
F4U-1A BuNo.17802
Accepted: August 30, 1943
Service History:
ADU / NAS Port Columbus, Ohio (shipped: September 2, 1943)
NAS San Diego, California (shipped: September 8, 1943)
VMF-217 (shipped: September 29, 1943)
VMF-122 (January 14, 1944)
stricken: May 31, 1944
_____________________________________________________________
F4U-1A BuNo.17803
Accepted: August 30, 1943
Delivered: September 2, 1943
Service History:
ADU / NAS Port Columbus, Ohio (shipped: September 2, 1943)
NAS San Diego, California (shipped: September 9, 1943)
VF-17 “Jolly Rogers” (September 27, 1943)
Pacific Theatre (November 1, 1943)
*gap in history record
unknown: (August 1944 – October 1944)
NAS San Diego, California – pool (November 27, 1944)
stricken: November 30, 1944
_____________________________________________________________
F4U-1A BuNo.17804
Accepted: August 31, 1943
Service History:
ADU / NAS New York, New York (shipped: September 6, 1943)
NAS San Diego, California (shipped: September 12, 1943)
NAS Pearl Harbor, Hawaii (September 29, 1943)
VF-17 “Jolly Rogers” (November 21, 1943)
stricken: December 11, 1943
_____________________________________________________________
F4U-1A BuNo.17805
Accepted: August 31, 1943
Delivered: September 6, 1943
Service History:
*gap in history record
VF-85 (August 1944)
CASU-23 (September 1944 – October 2, 1944)
VF-10 (October 2, 1944 – October 4, 1944)
VF-89 (October 4, 1944 – November 1944)
CASU-23 / NAS Atlantic City, New Jersey (November 1944)
VF-88 (December 1944 – January 1945)
ATU / NAS Quonset, Rhode Island (February 1945)
CASU-22 / NAS Quonset Point, Rhode Island (March 1945 – April 1945)
VBF-94B (May 1945)
MCAS Quantico, Virginia – awaiting reconditioning (June 1945)
MCAS Quantico, Virginia – under reconditioning (July 1945 - August 1945)
MCAS Quantico, Virginia – pool (September 1945 – October 31, 1945)
COMFAIRWEST (*probably never delivered)
NAS Clinton, Oklahoma
stricken: November 30, 1945
_____________________________________________________________
F4U-1A BuNo.17806
Accepted: August 31, 1943
Service History:
ADU / NAS Port Columbus, Ohio (shipped: September 2, 1943)
NAS San Diego, California (shipped: September 14, 1943)
Naumea, New Caledonia (shipped: September 30, 1943)
VMF-216 (shipped: December 19, 1943)
stricken: April 11, 1944
_____________________________________________________________
F4U-1A BuNo.17807
Accepted: August 31, 1943
Service History:
ADU / NAS New York, New York (shipped: September 6, 1943)
NAS San Diego, California (shipped: September 11, 1943)
Naumea, New Caledonia (shipped: September 30, 1943)
VMF-211 (shipped: January 14, 1944)
stricken: March 28, 1944
_____________________________________________________________
F4U-1A BuNo.17808
Accepted: August 31, 1943
Service History:
ADU / NAS Port Columbus, Ohio (shipped: September 2, 1943)
NAS San Diego, California (shipped: September 9, 1943)
Naumea, New Caledonia (shipped: September 27, 1943)
VMF-216 (shipped: November 27, 1943)
stricken: April 11, 1944
_____________________________________________________________
F4U-1A BuNo.17809
Accepted: August 31, 1943
Delivered: September 6, 1943
Service History:
*gap in history record
unknown (August 1944 – October 1944)
MCAS Quantico, Virginia – Assembly & Repair (November 1944 – February 1945)
VBF-150 (February 1945)
MCAS Quantico, Virginia - awaiting reconditioning (March 1945 – May 18, 1945)
Elizabeth, North Carolina (May 21, 1945 – May 21, 1945)
CASU-24 / NAS Wildwood, New Jersey (May 1945)
VMF-911 (June 1945 – September 1945)
NAS Clinton, Oklahoma – pool
stricken: October 31, 1945